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Journal Articles ESAIM: Control, Optimisation and Calculus of Variations Year : 2018

Shape optimization via a levelset and a Gauss-Newton method

Abstract

In the context of shape optimization via level-set methods, we propose a general framework for a Gauss-Newton method to optimize quadratic functionals. Our approach provides a natural extension of the shape derivative as a vector field defined in the whole working domain. We implement and discuss this method in two cases: first a least-square error minimization reminiscent of the Electrical Impedance Tomography problem, and second the compliance problem with volume constraints.
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Dates and versions

hal-01880769 , version 1 (25-09-2018)

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Frédéric de Gournay, Jérôme Fehrenbach. Shape optimization via a levelset and a Gauss-Newton method. ESAIM: Control, Optimisation and Calculus of Variations, inPress, ⟨10.1051/cocv/2017014⟩. ⟨hal-01880769⟩
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